OK, a little tree biology is in order. All trees of any size, conifers
included, can develop extremely widespreading root systems. A rule of thumb
is a spread twice the height of the canopy - a 60' tree can have roots that
spread in a diameter of 120' or more. In certain deciduous trees and
conifers, those root systems can be very dense as well and they can indeed
outcompete smaller plants for soil moisture and nutrients just by virtue of
their volume and spread. Plants which typically grow as woodland understory
plantings are adapted to these conditions and are generally not fussy about
soils or water. More cultivated ornamentals and certainly any annuals (like
most veggies) are not happy and will not thrive in these conditions, needing
more sun, soil fertility and water than a location adjacent to a large tree
can provide.

I won't get into the legal issues involved in consciously damaging or
killing a tree located on another's property - they differ regionally and
can be significant. Deal with what you have - that is one of the challenges
of good gardening. Plant the veggies or whatever in an area well away from
the root system. Raised beds may work well.

pam - gardengal